# To Spray or Not to Spray: A Decision Analysis of Coffee Berry Borer in Hawaii

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Optimization Model

#### 2.1. Infestation Level

#### 2.2. Harvest Rate

#### 2.3. Net Benefit

## 3. Empirical Decision Tree Model

^{®}[30] (Frontline Systems Inc., Incline Village, NV, USA), which is a Microsoft Excel Add-In. This software was chosen for its ease of use and familiarity for farmers. The parameters for a farm are assigned to cells used in a spreadsheet, and the decision tree takes each node and applies the equations for infestation level, harvest, and net benefit. Three separate trees are mapped out as discussed by the theoretical equations.

## 4. Results

#### 4.1. Simulation Study 1: Minimizing Initial Infestation

#### 4.2. Simulation Study 2: Impact of Subsidy

## 5. Robustness Checks

#### 5.1. Sensitivity Analysis

#### 5.2. Breakeven Analysis

## 6. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CBB | Coffee Berry Borer |

USDA | United States Department of Agriculture |

IPM | Integrated Pest Management |

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**Figure 1.**Scenario 1 with 1% initial infestation, last two periods: this figure is a close-up of a decision tree and the final two periods based on scenario 1 in the text. The squares represent a decision to spray (

**up**) and not spray (

**down**). The numbers below represent the net benefit for that period based on the decision. The left triangle is the end point, or final month of December, with the number representing the total net benefit. The black line represents the optimal decision path.

**Figure 2.**Scenario 2 with 6% initial infestation, last two periods: this figure is a close-up of a decision tree and the final two periods based on scenario 2 in the text. The squares represent a decision to spray (

**up**) and not spray (

**down**). The numbers below represent the net benefit for that period based on the decision. The left triangle is the end point, or final month of December, with the number representing the total net benefit. The black line represents the optimal decision path.

**Figure 3.**Spider Plot Showing Percentage Change in Net Benefit: This figure shows the change in net benefit as spray effectiveness, spray cost, infestation level, and growth rate changes from +/− 100%.

Divisor (Per) | Unit | Range | Average | |
---|---|---|---|---|

Acres | Acres | 0–3100 | 1.67 | |

Projected Cherry | Acre | Lbs. | 0–10,000 | 7500 |

Farm Labor | Hour | Dollars | 0–30 | 15 |

Spray Labor | Acre | Hours | 0–2 | 1 |

Harvest labor | Lbs. | Dollars | 0–2 | 0.5 |

Pesticide | Acre | Quart | 0–2 | 1 |

Pesticide Costs | Quart | Dollars | 0–100 | 70.35 |

Water | Acre | Gallons | 0–200 | 100 |

Water Cost | 1k Gallon | Dollars | 0–2 | 1 |

Surfactant | Acre | Ounces | 0–100 | 45 |

Surfactant Costs | Quart | Dollars | 0–20 | 8 |

Harvest Rate | Period | Percentage | 0–100 | 25 |

Cherry Price | Lbs. | Dollars | 0–2.5 | 2 |

Unit | Range | Average | |
---|---|---|---|

Initial Infestation | % | 0–10 | 1 |

Spray Effectiveness | % | 0–100 | 50 |

Growth Rate | % | 0–100 | 35 |

Scenario 1 (Low Rate) | Scenario 2 (High Rate) | Difference | |
---|---|---|---|

Initial infestation level | 1% | 6% | 5% |

Total NB (Optimal Path) | $15,478.09 | $8716.95 | $6761.14 |

Total NB (Spray) | $15,316.05 | $8716.95 | $6599.10 |

Scenario 1 (No Subsidy) | Scenario 2 (w/Subsidy) | Difference | |
---|---|---|---|

Pesticide Cost (per acre) | $70.35 | $15.00 | $55.35 |

Pesticide Cost (per month) | $117.48 | $25.05 | $92.43 |

Total NB (Optimal) | $15,478.09 | $16,425.26 | $947.17 |

Total NB (no spray final period) | $15,478.09 | $16,402.43 | $924.34 |

Min | Max | Base | Pessimistic Scenario | Optimistic Scenario | |
---|---|---|---|---|---|

Cherry Price | $1.00 | $2.00 | $2.00 | $1.50 | $2.00 |

Spray Cost | $0 | $100.00 | $70.35 | $70.35 | $70.35 |

Infestation Level | 1% | 20% | 1% | 4% | 1% |

Spray Effectiveness | 30% | 80% | 50% | 40% | 50% |

CBB Growth Rate | 0% | 100% | 35% | 50% | 25% |

Initial Infestation | Net Benefit |
---|---|

0% | $16,635.87 |

1% | $15,246.59 |

2% | $13,857.30 |

5% | $9689.45 |

10% | $2743.04 |

12% | $1353.75 |

12.6% | $0.00 |

15% | −$3161.42 |

20% | −$9760.51 |

Spray Effectiveness | Net Benefit | Final Inf. Level | Net Harvests (Lbs.) |
---|---|---|---|

0% | $13,985.90 | 24% | 10,124 |

25% | $14,245.52 | 17% | 10,792 |

50% | $14,478.09 | 7.6% | 11,767 |

75% | $16,257.25 | 5.5% | 11,977 |

100% | $16,778.18 | 2.9% | 12,238 |

Pesticide Cost (per qt) | Optimal Net Benefit | Final Inf. Level | Net Harvest (Lbs.) |
---|---|---|---|

$0.00 | $16,725.86 | 6.0% | 11,865 |

$15.00 | $16,425.26 | 6.0% | 11,865 |

$20.40 | $16,317.05 | 6.0% | 11,865 |

$50.00 | $15,817.93 | 7.6% | 11,767 |

$70.35 | $15,478.09 | 7.6% | 11,767 |

$100.00 | $14,982.93 | 7.6% | 11,767 |

Difference | |||

70.35-0 | $1247.77 | ||

100.00-0 | $1742.93 |

Spray Cost | Initial Infestation |

$0.00 | 13.67% |

$25.00 | 13.29% |

$50.00 | 12.91% |

$75.00 | 12.53% |

$100.00 | 12.15% |

Spray Effectiveness | Initial Infestation |

0% | 3.47% |

25% | 6.38% |

50% | 12.61% |

75% | 27.27% |

100% | 66.41% |

Variable | Base | Breakeven |
---|---|---|

Pesticide Cost | $70.35 | $834.62 |

Initial Infestation | 1.00% | 12.60% |

Spray Effectiveness | 50% | −59.69% |

Growth Rate | 35% | 112% |

Price | $2.00 | $0.71 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Woodill, A.J.; Nakamoto, S.T.; Kawabata, A.M.; Leung, P.
To Spray or Not to Spray: A Decision Analysis of Coffee Berry Borer in Hawaii. *Insects* **2017**, *8*, 116.
https://doi.org/10.3390/insects8040116

**AMA Style**

Woodill AJ, Nakamoto ST, Kawabata AM, Leung P.
To Spray or Not to Spray: A Decision Analysis of Coffee Berry Borer in Hawaii. *Insects*. 2017; 8(4):116.
https://doi.org/10.3390/insects8040116

**Chicago/Turabian Style**

Woodill, A. John, Stuart T. Nakamoto, Andrea M. Kawabata, and PingSun Leung.
2017. "To Spray or Not to Spray: A Decision Analysis of Coffee Berry Borer in Hawaii" *Insects* 8, no. 4: 116.
https://doi.org/10.3390/insects8040116